Secret sharing via blockchains

CROSS-REFERENCE TO RELATED APPLICATIONS

0001This patent application is a continuation of U.S. application Ser. No. 15/435,612 filed Feb. 17, 2017 and since issued as U.S. Pat. No. 10,411,897, which is incorporated herein by reference in its entirety. This patent application also relates to U.S. application Ser. No. 15/419,033 filed Jan. 30, 2017, since issued as U.S. Pat. No. 10,419,225, and to U.S. application Ser. No. 15/419,042 also filed Jan. 30, 2017 (since abandonded), with both patent applications incorporated herein by reference in their entireties.

BACKGROUND

0002Security is important in today's online environment. One reads nearly every day of another hacking. People's data is even being held ransom.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The features, aspects, and advantages of the exemplary embodiments are understood when the following Detailed Description is read with reference to the accompanying drawings, wherein:

<figref idref="DRAWINGS">FIGS. 1-3</figref> are simplified illustrations for secretly sharing an electronic document, according to exemplary embodiments;

<figref idref="DRAWINGS">FIG. 4</figref> is a detailed illustration of an operating environment, according to exemplary embodiments;

<figref idref="DRAWINGS">FIGS. 5-6</figref> illustrate hashing, according to exemplary embodiments;

<figref idref="DRAWINGS">FIGS. 7-8</figref> illustrate a sharing strategy, according to exemplary embodiments;

<figref idref="DRAWINGS">FIGS. 9-10</figref> are flowcharts illustrating methods or algorithms for secret sharing via blockchain(s), according to exemplary embodiments; and

<figref idref="DRAWINGS">FIGS. 11-12</figref> depict still more operating environments for additional aspects of the exemplary embodiments.

DETAILED DESCRIPTION

0010The exemplary embodiments will now be described more fully hereinafter with reference to the accompanying drawings. The exemplary embodiments may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. These embodiments are provided so that this disclosure will be thorough and complete and will fully convey the exemplary embodiments to those of ordinary skill in the art. Moreover, all statements herein reciting embodiments, as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents as well as equivalents developed in the future (i.e., any elements developed that perform the same function, regardless of structure).

0011Thus, for example, it will be appreciated by those of ordinary skill in the art that the diagrams, schematics, illustrations, and the like represent conceptual views or processes illustrating the exemplary embodiments. The functions of the various elements shown in the figures may be provided through the use of dedicated hardware as well as hardware capable of executing associated software. Those of ordinary skill in the art further understand that the exemplary hardware, software, processes, methods, and/or operating systems described herein are for illustrative purposes and, thus, are not intended to be limited to any particular named manufacturer.

0012As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless expressly stated otherwise. It will be further understood that the terms “includes,” “comprises,” “including,” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element or intervening elements may be present. Furthermore, “connected” or “coupled” as used herein may include wirelessly connected or coupled. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.

0013It will also be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first device could be termed a second device, and, similarly, a second device could be termed a first device without departing from the teachings of the disclosure.

0014<figref idref="DRAWINGS">FIGS. 1-3</figref> are simplified illustrations for secretly sharing an electronic document <b>20</b>, according to exemplary embodiments. The electronic document <b>20</b> contains sensitive information, such as a user's social security number, income, banking, and other personal information. The electronic document <b>20</b>, in plain words, contains secret data <b>22</b>. While the electronic document <b>20</b> may have any content, most readers are thought familiar with a mortgage application <b>24</b>. That is, the electronic document <b>20</b> may be a web-based, portable document format (PDF) associated with an applicant's personal and financial records for obtaining a mortgage. As the reader understands, the mortgage application <b>24</b> includes the secret data <b>22</b>, such as an applicant's social security number, income, and banking records. If the mortgage application <b>24</b> were to fall into the wrong hands, the secret data <b>22</b> may be nefariously used by a rogue entity.

0015Exemplary embodiments thus protect the secret data <b>22</b>. A server <b>26</b> retrieves a representation <b>28</b> of the electronic document <b>20</b> and splits the representation <b>28</b> into multiple pieces termed shares <b>30</b>. The server <b>26</b> may then distribute one or more of the shares <b>30</b> via a blockchain <b>32</b>. As the reader may understand, the blockchain <b>32</b> is generally a digital ledger in which transactions are chronologically and/or publically recorded. The blockchain <b>32</b> is most commonly used in decentralized cryptocurrencies (such as Bitcoin). The blockchain <b>32</b>, however, may be adapted to any chain or custody (such as in medical records and in chains of title in real estate transactions). Indeed, there are many different mechanisms and configurations of the blockchain <b>32</b>, and exemplary embodiments may be adapted to any version. Regardless, the shares <b>30</b> may be integrated into the blockchain <b>32</b> as a distribution or publication mechanism. The blockchain <b>32</b> may then route via a communications network <b>34</b> to any destination.

0016<figref idref="DRAWINGS">FIG. 2</figref> illustrates secret sharing. Once the representation <b>28</b> of the electronic document <b>20</b> is split into the multiple shares <b>30</b>, the server <b>26</b> may integrate any one or more of the shares <b>30</b> into the blockchain <b>32</b>, perhaps with a timestamp <b>40</b>. While the blockchain <b>32</b> may be sent or routed to any destination (such as an Internet Protocol address associated with another server or device), <figref idref="DRAWINGS">FIG. 2</figref> illustrates peer distribution. That is, the server <b>26</b> may broadcast the blockchain <b>32</b> to the IP addresses associated with a group <b>42</b> of peer devices or nodes. The blockchain <b>32</b>, in other words, is distributed to trusted peers for further processing and/or verification.

0017<figref idref="DRAWINGS">FIG. 3</figref> further illustrates secret sharing. Here the server <b>26</b> may integrate any one or more of the shares <b>30</b> into multiple blockchains <b>32</b>. While exemplary embodiments may utilize any number of different blockchains <b>32</b>, <figref idref="DRAWINGS">FIG. 3</figref> illustrates a simple example of three (3) blockchains <b>32</b><i>a</i>-<i>c </i>distributed to three (3) different groups <b>42</b><i>a</i>-<i>c </i>of peer devices. That is, some of the shares <b>30</b> (such as a first subset <b>50</b>) are integrated into a first blockchain <b>32</b><i>a </i>and distributed (via the communications network <b>34</b> illustrated in <figref idref="DRAWINGS">FIGS. 1-2</figref>) to a first group <b>42</b><i>a </i>of peer devices. A second subset <b>52</b> of the shares <b>30</b> are integrated into a second blockchain <b>32</b><i>b </i>and distributed to a second group <b>42</b><i>b </i>of peer devices. Still more shares <b>30</b> (such as the remaining portion or pieces in a third subset <b>54</b>) are integrated into a third blockchain <b>32</b><i>c </i>and distributed to a third group <b>42</b><i>c </i>of peer devices. Different collections of the shares <b>30</b>, in other words, may be distributed via different blockchains <b>32</b> to different peer devices.

0018Exemplary embodiments may thus stash the secret data <b>22</b> in the multiple blockchains <b>32</b><i>a</i>-<i>c</i>. Because the electronic document <b>20</b> (containing the secret data <b>22</b>) is split into the multiple shares <b>30</b>, any one or more of the peer devices must possess a sufficient minimum number M_Min(illustrated as reference numeral <b>60</b>) of the shares <b>30</b> before the secret data <b>22</b> may be recovered. That is, possession of an insufficient number of the shares <b>30</b> guarantees that the secret data <b>22</b> remains unknown and confidential. So, if the first blockchain <b>32</b><i>a </i>contains less than the M_Min<b>60</b> of the total shares <b>30</b>, then the first group <b>42</b><i>a </i>of peer devices cannot reconstruct the secret data <b>22</b>. Likewise, if the second blockchain <b>32</b><i>b </i>and/or the third blockchain <b>32</b><i>c </i>also contains less than the M_Min<b>30</b>, the second group <b>42</b><i>b </i>of peer devices and the third group <b>42</b><i>c </i>of peer devices are also unable to reveal or decipher the secret data <b>22</b>. In other words, no single one of the multiple blockchains <b>32</b><i>a</i>-<i>c </i>stores the requisite minimum number M_Min<b>60</b> of the shares <b>30</b> to launch a brute-force attack on the secret data <b>22</b>. Even multiple ones of the blockchains <b>32</b><i>a</i>-<i>c </i>may be purposefully designed to never exceed the requisite minimum number M_Min<b>60</b> of the shares <b>30</b>, perhaps thus forcing a hacker to compromise several or all of the blockchains <b>32</b><i>a</i>-<i>c</i>. A rogue attack, in simple words, would have to access and compromise multiple blockchains <b>32</b> before jeopardizing the secret data <b>22</b> contained within the electronic document <b>20</b>.

0019Exemplary embodiments thus present an elegant solution. Sensitive, secret documents (containing the secret data <b>22</b>) may be secretly shared via the one or more blockchains <b>32</b><i>a</i>-<i>c</i>. Even if the blockchains <b>32</b><i>a</i>-<i>c </i>are dispersed to trusted peer devices, the peer devices still cannot discern the secret data <b>22</b> until the threshold minimum number M_Min<b>60</b> of the shares <b>30</b> is obtained. Exemplary embodiments thus purposefully add a second-layer of protection, beyond merely trusted receipt of the blockchain <b>32</b>. The trusted peers simply do not have access to the secret data <b>22</b> until the minimum number M_Min<b>60</b> of the shares <b>30</b> is obtained.

0020Any secret sharing scheme may be utilized. The reader is perhaps familiar with Shamir's Secret Sharing Algorithm, which is a well-known cryptographic algorithm. Exemplary embodiments divide the secret data <b>22</b> into unique parts (e.g., the shares <b>30</b>), with each individual share <b>30</b> being different from other shares <b>30</b>. However, there are many secret sharing or splitting schemes and algorithms for distributing a secret, and exemplary embodiments may be applied regardless of any particular scheme or algorithm.

0021<figref idref="DRAWINGS">FIG. 4</figref> is a detailed illustration of an operating environment, according to exemplary embodiments. Here the server <b>26</b> secretly shares the electronic document <b>20</b> via the one or more blockchains <b>32</b>. The server <b>26</b> may have a processor <b>70</b> (e.g., “μP”), application specific integrated circuit (ASIC), or other component that executes an electronic representation of a sharing algorithm <b>72</b> stored in a local memory device <b>74</b>. The sharing algorithm <b>72</b> includes instructions, code, and/or programs that cause the server <b>26</b> to perform operations, such as splitting or segmenting the representation <b>28</b> of the electronic document <b>20</b> into the multiple shares <b>30</b>. The sharing algorithm <b>72</b> may then select one or more of the shares <b>30</b> (such as the first subset <b>50</b>) for integration into the first blockchain <b>32</b><i>a</i>. The sharing algorithm <b>72</b> may then select other ones of the shares <b>30</b> (such as the second subset <b>52</b>) for integration into the second blockchain <b>32</b><i>b</i>. The sharing algorithm <b>72</b> may then integrate any remaining, unselected ones of the shares <b>30</b> (such as the third subset <b>54</b>) for integration into the third blockchain <b>32</b><i>c</i>. The sharing algorithm <b>72</b> may also add the timestamp <b>40</b> to each blockchain <b>32</b><i>a</i>-<i>c</i>. After different collections of the shares <b>30</b> are integrated into the different blockchains <b>32</b><i>a</i>-<i>c</i>, the blockchains <b>32</b><i>a</i>-<i>c </i>are distributed to their respective destinations (such as Internet Protocol addresses associated with the first group <b>42</b><i>a </i>of peer devices, the second group <b>42</b><i>b </i>of peer devices, and the third group <b>42</b><i>c </i>of peer devices).

0022Exemplary embodiments may be applied regardless of networking environment. Exemplary embodiments may be easily adapted to stationary or mobile devices having cellular, wireless fidelity (WI-FI®), near field, and/or BLUETOOTH® capability. Exemplary embodiments may be applied to mobile devices utilizing any portion of the electromagnetic spectrum and any signaling standard (such as the IEEE 802 family of standards, GSM/CDMA/TDMA or any cellular standard, and/or the ISM band). Exemplary embodiments, however, may be applied to any processor-controlled device operating in the radio-frequency domain and/or the Internet Protocol (IP) domain. Exemplary embodiments may be applied to any processor-controlled device utilizing a distributed computing network, such as the Internet (sometimes alternatively known as the “World Wide Web”), an intranet, a local-area network (LAN), and/or a wide-area network (WAN). Exemplary embodiments may be applied to any processor-controlled device utilizing power line technologies, in which signals are communicated via electrical wiring. Indeed, exemplary embodiments may be applied regardless of physical componentry, physical configuration, or communications standard(s).

0023Exemplary embodiments may utilize any processing component, configuration, or system. Any processor could be multiple processors, which could include distributed processors or parallel processors in a single machine or multiple machines. The processor can be used in supporting a virtual processing environment. The processor could include a state machine, application specific integrated circuit (ASIC), programmable gate array (PGA) including a Field PGA, or state machine. When any of the processors execute instructions to perform “operations”, this could include the processor performing the operations directly and/or facilitating, directing, or cooperating with another device or component to perform the operations.

0024Exemplary embodiments may packetize. The server <b>26</b> and the recipient peer devices may have network interfaces to the communications network <b>34</b>, thus allowing collection and retrieval of information. The information may be received as packets of data according to a packet protocol (such as the Internet Protocol). The packets of data contain bits or bytes of data describing the contents, or payload, of a message. A header of each packet of data may contain routing information identifying an origination address and/or a destination address.

0025<figref idref="DRAWINGS">FIGS. 5-6</figref> illustrate hashing, according to exemplary embodiments. When the server <b>26</b> retrieves the representation <b>28</b> of the electronic document <b>20</b>, here the representation <b>28</b> may be one or more hash values <b>80</b>. That is, the server <b>26</b> may call or invoke an electronic representation of a hashing algorithm <b>82</b> that hashes electronic data <b>84</b> representing or associated with the electronic document <b>20</b> to generate the hash values <b>80</b>. The hash values <b>80</b> may be associated with a hash tree <b>86</b> and/or root <b>88</b>. The sharing algorithm <b>72</b> may then retrieve and split the hash values <b>80</b> into the multiple shares <b>30</b>. The sharing algorithm <b>72</b> may then group or collect different ones of the shares <b>30</b> for integration into the one or more blockchains <b>32</b> (as this disclosure earlier explained). The blockchains <b>32</b> are then distributed to their respective destinations (again as this disclosure earlier explained). Exemplary embodiments may thus first hash the electronic document <b>20</b>, create the shares <b>30</b> from the hash values <b>80</b>, and then integrate the shares <b>30</b> into the blockchain(s) <b>32</b>.

0026Hashing adds another layer of security. Exemplary embodiments may call or execute the hashing algorithm <b>82</b> that generates the hash values <b>80</b> (e.g., the hash tree <b>86</b> and the root <b>88</b>) associated with the electronic document <b>20</b>. There are many hashing algorithms, and exemplary embodiments may utilize any of the hashing algorithms. For example, many readers may be familiar with the SHA family of cryptographic hashing algorithms. Moreover, the hash tree <b>86</b> may be described as the Merkle tree, which many readers are also thought familiar. Regardless, once the hash values <b>80</b> are determined, exemplary embodiments may split the hash values <b>80</b> into the shares <b>30</b> for integration into the one or more blockchains <b>32</b>. That is, the shares <b>30</b> may be added to, or incorporated in, any record, transaction, or block and distributed via the blockchain(s) <b>32</b>.

0027<figref idref="DRAWINGS">FIG. 6</figref> illustrates an alternative hashing strategy. Here the server <b>26</b> may call or invoke the sharing algorithm <b>72</b> to split the electronic data <b>84</b> associated with the electronic document <b>20</b> into the multiple shares <b>30</b>. The server <b>26</b> may then apply the hashing algorithm <b>82</b> to the shares <b>30</b> to generate the hash values <b>80</b>. The hash values <b>80</b> may then be integrated into the one or more blockchains <b>32</b> for distribution. Exemplary embodiments may thus first create the shares <b>30</b> from the electronic data <b>84</b>, hash the shares <b>30</b>, and then integrate the hash values <b>80</b> into the blockchain(s) <b>32</b>.

0028<figref idref="DRAWINGS">FIGS. 7-8</figref> illustrate a sharing strategy <b>90</b>, according to exemplary embodiments. Here the sharing algorithm <b>72</b> may retrieve and implement the sharing strategy <b>90</b> that defines distribution via the multiple blockchains <b>32</b><i>a</i>-<i>c </i>to protect the secret data <b>22</b>. Suppose, for example, that the total number N_S(illustrated as reference numeral <b>92</b>) of the shares <b>30</b> defines a number N_B(illustrated as reference numeral <b>94</b>) of the different blockchains <b>32</b>. The total number N_S<b>92</b> of the shares <b>30</b>, in other words, may relate by a ratio to the number N_B<b>94</b> of blockchains <b>32</b> that must be used. As a simple example, the ratio may be

0029<maths id="MATH-US-00001" num="00001"><math overflow="scroll"><mrow><mrow><mfrac><msub><mi>N</mi><mi>S</mi></msub><msub><mi>N</mi><mi>B</mi></msub></mfrac><mo>=</mo><mrow><mn>10</mn><mo>⁢</mo><mstyle><mtext>,</mtext></mstyle><mo>⁢</mo><mn>000</mn></mrow></mrow><mo>,</mo></mrow></math></maths><img file="US11296889B2_D0001.tif" /><img file="US11296889B2_D0002.tif" /><br /> where the total number N_S<b>92</b> of the shares <b>30</b> is ten thousand (10,000) times the number N_B<b>94</b> of blockchains <b>32</b> that must be used. Again, as a simple example, if the electronic document <b>20</b> is associated with one million (1,000,000) shares <b>30</b>, then one hundred (100) different blockchains <b>32</b> must be generated and distributed. The sharing strategy <b>90</b>, in other words, may set a maximum number N_Smax(illustrated as reference numeral <b>96</b>) of shares <b>30</b> integrated into any single blockchain <b>32</b>. The sharing strategy <b>90</b>, in other words, may thus limit the number of the shares <b>30</b> exposed by any individual blockchain <b>32</b>.

0030<figref idref="DRAWINGS">FIG. 8</figref> further illustrates the sharing strategy <b>90</b>. Here, though, the number N_B<b>94</b> of blockchains may be based on the number of recipients. That is, the total number N_R(illustrated as reference numeral <b>98</b>) of the recipients may define the number N_B<b>94</b> of the different blockchains <b>32</b>. The greater the recipients, in other words, then the greater the N_B<b>94</b> of blockchains <b>32</b> that must be used. Again, suppose that the sharing strategy <b>90</b> may again be defined as the ratio

0031<maths id="MATH-US-00002" num="00002"><math overflow="scroll"><mrow><mrow><mfrac><msub><mi>N</mi><mi>R</mi></msub><msub><mi>N</mi><mi>B</mi></msub></mfrac><mo>=</mo><mn>100</mn></mrow><mo>,</mo></mrow></math></maths><img file="US11296889B2_D0003.tif" /><img file="US11296889B2_D0004.tif" /><br /> where the total number N_R<b>98</b> of the recipients is one hundred (100) times the number N_B<b>94</b> of blockchains <b>32</b> that must be used. Again, as a simple example, if there are ten thousand recipients, then one hundred (100) different blockchains <b>32</b> must be generated and distributed. The sharing strategy <b>90</b>, in other words, may set a maximum number N_Rmax(illustrated as reference numeral <b>100</b>) of recipients per blockchain <b>32</b>. The sharing strategy <b>90</b>, in other words, may thus limit the number of the shares <b>30</b> exposed by any individual blockchain <b>32</b>.

0032The sharing strategy <b>90</b> may be implemented as logical rules. If the sharing strategy <b>90</b> is mathematically defined (such as the ratio above discussed), the sharing strategy <b>90</b> may be expressed as logical statements involving mathematical expressions. Exemplary embodiments may code or program the sharing strategy <b>90</b> to achieve policy goals and/or security objectives.

0033<figref idref="DRAWINGS">FIG. 9</figref> is a flowchart illustrating a method or algorithm for secret sharing via the blockchain(s) <b>32</b>, according to exemplary embodiments. The electronic data <b>84</b> representing the electronic document <b>20</b> is received (Block <b>200</b>). The electronic data <b>84</b> is hashed using the hashing algorithm <b>82</b> (Block <b>202</b>) to generate the hash values <b>80</b> (Block <b>204</b>). The shares are created from the hash values <b>80</b> (Block <b>206</b>). The shares <b>30</b> are integrated into the one or more blockchains <b>32</b> (Block <b>208</b>).

0034<figref idref="DRAWINGS">FIG. 10</figref> is another flowchart illustrating a method or algorithm for secret sharing via the blockchain(s) <b>32</b>, according to exemplary embodiments. The electronic data <b>84</b> representing the electronic document <b>20</b> is received (Block <b>200</b>). The electronic data <b>84</b> is split to create the shares <b>30</b> (Block <b>202</b>). The shares <b>30</b> are hashed using the hashing algorithm <b>82</b> (Block <b>204</b>) to generate the hash values <b>80</b> (Block <b>206</b>). The hash values <b>80</b> are integrated into the one or more blockchains <b>32</b> (Block <b>208</b>).

0035<figref idref="DRAWINGS">FIG. 11</figref> is a schematic illustrating still more exemplary embodiments. <figref idref="DRAWINGS">FIG. 11</figref> is a more detailed diagram illustrating a processor-controlled device <b>250</b>. As earlier paragraphs explained, the sharing algorithm <b>72</b> and the hashing algorithm <b>82</b> may partially or entirely operate in any mobile or stationary processor-controlled device. <figref idref="DRAWINGS">FIG. 11</figref>, then, illustrates the sharing algorithm <b>72</b> and the hashing algorithm <b>82</b> stored in a memory subsystem of the processor-controlled device <b>250</b>. One or more processors communicate with the memory subsystem and execute either, some, or all applications. Because the processor-controlled device <b>250</b> is well known to those of ordinary skill in the art, no further explanation is needed.

0036<figref idref="DRAWINGS">FIG. 12</figref> depicts other possible operating environments for additional aspects of the exemplary embodiments. <figref idref="DRAWINGS">FIG. 12</figref> illustrates the sharing algorithm <b>72</b> and the hashing algorithm <b>82</b> operating within various other processor-controlled devices <b>250</b>. <figref idref="DRAWINGS">FIG. 12</figref>, for example, illustrates that the sharing algorithm <b>72</b> and the hashing algorithm <b>82</b> may entirely or partially operate within a set-top box (“STB”) (<b>252</b>), a personal/digital video recorder (PVR/DVR) <b>254</b>, a Global Positioning System (GPS) device <b>256</b>, an interactive television <b>258</b>, a tablet computer <b>260</b>, or any computer system, communications device, or processor-controlled device utilizing any of the processors above described and/or a digital signal processor (DP/DSP) <b>262</b>. Moreover, the processor-controlled device <b>250</b> may also include wearable devices (such as watches), radios, vehicle electronics, clocks, printers, gateways, mobile/implantable medical devices, and other apparatuses and systems. Because the architecture and operating principles of the various devices <b>250</b> are well known, the hardware and software componentry of the various devices <b>250</b> are not further shown and described.

0037Exemplary embodiments may be applied to any signaling standard. Most readers are thought familiar with the Global System for Mobile (GSM) communications signaling standard. Those of ordinary skill in the art, however, also recognize that exemplary embodiments are equally applicable to any communications device utilizing the Time Division Multiple Access signaling standard, the Code Division Multiple Access signaling standard, the “dual-mode” GSM-ANSI Interoperability Team (GAIT) signaling standard, or any variant of the GSM/CDMA/TDMA signaling standard. Exemplary embodiments may also be applied to other standards, such as the I.E.E.E. 802 family of standards, the Industrial, Scientific, and Medical band of the electromagnetic spectrum, BLUETOOTH®, and any other.

0038Exemplary embodiments may be physically embodied on or in a computer-readable storage medium. This computer-readable medium, for example, may include CD-ROM, DVD, tape, cassette, floppy disk, optical disk, memory card, memory drive, and large-capacity disks. This computer-readable medium, or media, could be distributed to end-subscribers, licensees, and assignees. A computer program product comprises processor-executable instructions for sharing secrets via blockchains, as the above paragraphs explained.

0039While the exemplary embodiments have been described with respect to various features, aspects, and embodiments, those skilled and unskilled in the art will recognize the exemplary embodiments are not so limited. Other variations, modifications, and alternative embodiments may be made without departing from the spirit and scope of the exemplary embodiments.